The effects of nanoparticles on the physical properties of type I collagen : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Chemistry at Massey University, Palmerston North, New Zealand

This thesis concerned with the interactions of surface functionalized TiO2 and ZnO NPs with type I collagen. The collagen nanocomposites formed with TiO2 and ZnO NPs may be potential candidates for some biomedical applications thanks to the synergetic effects between two materials. How the physical properties of collagen have been changed when interacting with TiO2 and ZnO NPs has been investigated in this project. The general background and research objectives of this study are introduced in Chapter 1, followed by Chapter 2 which gives details about the preparation of the samples, in addition to the characterization techniques and protocols. The TiO2 and ZnO NPs were synthesized by colloidal synthetic methods and their surfaces were functionalized with different functional groups. The physical properties of the TiO2-collagen nanocomposites and ZnO-induced collagen gels were studied by rheology, DSC, swelling ratio assay, FTIR and confocal microscopy. The mechanical studies are the main focus of this thesis. In Chapter 3, TiO2 NPs coated with chitosan and PAA were introduced into collagen solutions before fibrillogenesis was carried out. They were found to affect the linear rheology of the collagen gels as a function of their concentration. There were no significant differences in the strain-stress response in the non-linear rheology. It was found that the PAA coated TiO2 NPs promoted collagen fibrillogenesis, resulting in thin fibrils, and a dense and more crosslinked structure, while the chitosan coated TiO2 NPs slowed down the collagen fibrillogenesis and created a heterogeneous network with thick fibrils and less crosslinks. ZnO-PVP NPs were found to induce collagen gelation without the use of the conventional fibrillogenesis involving gelation buffer, as reported in Chapter 4. The hydrogel formed with this method was found to be three times as strong as the gel formed with conventional gelation buffer at the same collagen concentration. Confocal images indicated those two gels have different molecular assembly states. A group of experiments showed ZnO acted as a neutralizing agent here to raise the pH of the collagen solution to the pH close to the isoelectric point of the collagen. Both the TiO2 and ZnO NP-collagen systems have demonstrated that different collagen networks can be created by the direct or indirect interactions between collagen monomer solution and the nanoparticles. By manipulating the assembly of collagen to design different networks, it is possible to achieve the physical properties required for different applications. The results are followed by the conclusions and future perspectives of this study

Cut-touching linear functionals in the conformal bootstrap

The modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial "swapping" property, allowing to swap infinite summation with the action of the functional in the conformal bootstrap sum rule. Swapping is easy to justify for the popular functionals involving finite sums of derivatives. However, it is far from obvious for "cut-touching" functionals, involving integration over regions where conformal block decomposition does not converge uniformly. Functionals of this type were recently considered by Mazac in his work on analytic derivation of optimal bootstrap bounds. We derive general swapping criteria for the cut-touching functionals, and check in a few explicit examples that Mazac's functionals pass our criteria.Comment: 19 pages, 7 figures, v2: author order corrected, v3: full domain of 4pt analyticity made more precise, v4: misprint corrected and acknowledgement adde

A tauberian theorem for the conformal bootstrap

For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(2,R)-invariant correlators (also known as 1d CFTs). It also puts on solid ground a part of the lightcone bootstrap analysis of the spectrum of operators of high spin and bounded twist in CFTs in d>2. In addition, a similar argument controls the spectral density asymptotics in large N gauge theories.Comment: 36pp; v2: refs and comments added, misprints correcte